# Defending Many Worlds via Case Discrimination: An Attempt to Showcase the Conceptual Incoherence of Anti-Realist Interpretations and Relational Quantum Mechanics

## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Juxtaposing QM Interpretations via Repeated Case Discriminations

#### 3.1. Anti-Realist Interpretations

#### 3.1.1. The Copenhagen Interpretation

“(simply) pointing to Born’s rule does not avoid the measurement problem”.

#### 3.1.2. QBism and the Problem of Truthmakers

“(A)ny viable (…) account of quantum mechanics will owe us another account of what the probabilities encoded in the quantum state are probabilities of, of what the physical features of systems are. Or, put in more pragmatic terms: what the non-quantum features of a system are such that the quantum state is a tool for answering questions about those features.”[2], (p. 12)

“one might also wonder how any theory that is not ψ-ontic could possibly account for interference phenomena, such as the Double-Slit experiment”.[15]

“In physics jargon, there is interference between the ψ_{x}and ψ_{y}parts of the state, so that the x outcome is reinforced and the y outcome is cancelled out; interference phenomena like this are very general, and rule out the possibility of a probabilistic interpretation of the state space.”[17], (p. 5, my emphasis)

“In any concrete instantiation of quantum theory, the observables over which probability distributions are defined are particle positions, field strengths, collective spins and the like. The only way to say anything non-circularly about an agent’s experience in quantum mechanics is to characterize it externally, as an experience of something describable in a more physical language. And then the problems confronted by (such) strategies, (…), reappear.”[2], (my emphasis)

“Explanations of, say, superconductivity, or the heat capacity of crystals, or the thermodynamic features of the quark-gluon plasma, or the colour of gold, or any of the thousands of concrete applications of quantum theory that form its real empirical base, seem out of reach for QBism, or for pragmatism, at least as they are currently stated.”[2]

“(…) just as it would be misleading to call classical statistical mechanics non-realist simply because the distribution function does not play a representational role, so would it be misleading to call these approaches to quantum probabilities, as QBist´s particularly tend to argue, non-realist simply because in those theories the quantum state does not play a representational role either.”[2]

#### 3.1.3. An Ontology of ‘Pure Experience’?

“My thesis is that if we start with the supposition that there is only one primal stuff or material in the world, a stuff of which everything is composed, and if we call that stuff ‘pure experience’, then knowing can easily be explained as a particular sort of relation towards one another into which portions of pure experience may enter. The relation itself is a part of pure experience; one of its ‘terms’ becomes the subject or bearer of the knowledge, the knower, the other becomes the object known”[19], (p. 32)

**Counterfactual**

**1.1.**

**Counterfactual**

**1.2.**

#### 3.1.4. An Ontology of Pure Information

#### 3.1.5. A Trilemma for the Anti-Realist

**Counterfactual**

**2.1.**

**Argument I.**

**AI.1.**

**AI.2.**

**AI.C.**

**AI.3.**

**AI.C2.**

**Counterfactual**

**2.2.**

**Argument II.**

**AII.1.**

**AII.2.**

**AII.C.**

**Counterfactual**

**2.3.**

**Argument III.**

**A.III.1.**

**A.III.2.**

**A.III.C.**

#### 3.1.6. Anti-Realist Interpretations: Preliminary Conclusion

- Ad. Counterfactual 2.1.: PE entails that reality is comprised entirely of Bayesian belief structures coupled to pure experience such that no structure is ontologically privileged or in some way selected.
- Ad. Counterfactual 2.2.: Information theoretic ‘anti-realist’ (e.g., informational QBist or neo-CI) interpretations have ultimately to be understood in terms of OSR such that they themselves in fact comprise an ontic structure of reality. Without adding mind-induced collapses or further hidden variables for state reduction or selection, thus having an egalitarian outlook at all possible eigenstates, these views collapse into OSR–MWI.The principle of conservation of information furthermore prohibits any arbitrary state-reduction.
- Ad. AI.C2 and AII.C: The difference between a Bayesian structure (without additional ontology) and an information-theoretic ontology becomes negligible. Hence OSR–MWI~PEMWI
- Given that many defenders of MWI very often have OSR leanings, it might ultimately also hold that OSR–MWI~PEMWI~MWI.
- Ad. Counterfactual 2.3.: Bayesian belief structures either require objective truthmakers and mind-independent mechanisms for state reduction or selection, which are themselves hidden variables, or, are structurally complete. If the former, hidden variables exist; if the latter, then it is as elaborated above, i.e., QBism → PEMWI~OSR–MWI~MWI.

- (a)
- empirically adequate, but in some sense, nomologically incomplete or
- (b)
- empirically adequate and nomological complete.

#### 3.2. Rovelli´s Relational Interpretation—MWI in Disguise?

“RQM is based on an ontology given by physical systems described by physical variables, as in classical mechanics. The difference with classical mechanics is that (a) variables take value only at interactions and (b) the values they take are only relative to the (other) system affected by the interaction. Here “relative” is in the same sense in which velocity is a property of a system relative to another system in classical mechanics (as opposed to “subjective”). The world is therefore described by RQM as an evolving network of sparse relative events, described by punctual relative values of physical variables.”[27], (emphasis & addition in brackets added)

“the interference observed by a system S′ is not erased by the actualization of variables relative to a different system S″”.[27]

**Counterfactual**

**3.**

- (a)
- either they are giving up the relational aspect of RQM, or,
- (b)
- they too are bound to accept MWI.

“Different observers can give different accounts of the same set of events”.[27]

The particular conjunction of variables an agent observes exists relative to the sum of all her physical interactions, i.e., to the whole web of physical relations involved. The latter, in turn, selects definite values for each quantum system that an interaction has occurred with. However, this sum total is not unique given that different ‘webs of variable values’ occur for different interacting systems. Furthermore, given that such web of objective physical interactions behave similar to a spreading entanglement (Rovelli uses the phrase of “an evolving network of sparse relative events”), it seems ultimately conceptually no different from a decoherence-induced emergent branch as according to MWI.

“Understood in this manner the quantum state is always and only a relative state in the sense of Everett. In this sense RQM is “Everettian”; it is so in a different sense than the Many Worlds interpretations, which are based on a realistic interpretation of the universal wave function, rejected in RQM.”.[27]

“(…) the interpretation had better not introduce a notion of privilege for one domain over another, in anything more than an interest-relative sense. Again, there is an analogy in the case of time: if we are to provide an interpretation of the “flow” of time, consistent with a relational account of tense, then it had better not lead to any “absolute” significance of one space-time foliation over another; and conversely, if we do have the latter, then there is no sense to the appeal to anthropocentric factors.”[29]

**Argument IV.**

**AIV.1.**

**AIV.2.**

**AIV.3.**

**AIV.4.**

**AIV.C**

**Proof**

**Sketch.**

#### 3.3. Bohmian Mechanics (BM) and Objective-Collapse Theories (OCT)

#### 3.3.1. Introducing BM and OCT

#### 3.3.2. General Challenges

“(…) the way Bohmian mechanics, and GRW theory, are normally discussed in philosophy of physics (especially in more metaphysical contexts) is sharply at odds with the relatively humble role non-relativistic particle mechanics plays in real quantum theory. The only way I know to make sense of (most of) this literature is to interpret it as discussing non-relativistic quantum particle mechanics under the fiction that it is a fundamental and universal theory.”.[2], (p. 43)

“parallel-universe theories in a state of chronic denial”.[34], (p. 225)

“GRWm is a theory about the behavior of a field m(·,t) on three-dimensional space. The microscopic description of reality provided by the matter density field m(·,t) is not particle-like but instead continuous, in contrast to the particle ontology of BM. This is reminiscent of Schrodinger’s early view of the wave ¨ function as representing a continuous matter field. But while Schrodinger was obliged to abandon his early view because of the tendency of the wave function to spread, the spontaneous wave function collapses built into the GRW theory tend to localize the wave function, thus counteracting this tendency and overcoming the problem.”

“even in the non-relativistic domain [GRW] is not fully satisfactory: manifestly, the collapse mechanism does not preserve the symmetries of the wavefunction, and so it is not compatible with the existence of identical particles”.[33], (p. 42, my emphasis)

#### 3.3.3. QFT and Particle Indiscernibility as Master Arguments against BM and OCTs

“(I)t is much harder than is generally recognized to construct a quantum-field-theory version of Bohmian mechanics or GRW theory and so confidence that such a theory even exists i[s] premature, because most of the features of nonrelativistic quantum theory appealed-to by metaphysicians of quantum mechanics are emergent approximations at best in QFT.”[2], (p. 19)

“one might think that a field configuration would represent a particle configuration in some way, e.g., by distinguished “bump configurations” in the field. But that does not work out.”

“Fermions are not conducive to a naïve field ontology, while bosons are”[14]

“(…) bosons are commonly viewed as particles. For example, think of photons, the quanta of electromagnetic fields. A first thought might once again be that we should “see” the bosons in the field configuration as “bumps” in the field. But that is also more or less impossible.”[14]

“so a fundamental ontology based on the positions of particles looks forlorn in quantum field theory.”[37], (p. 5)

“OSR agrees with Cassirer that the field is nothing but structure.”[21], (p. 153)

“coincidences of field values, and complexes of relations among them—(…) is a world understood in terms of structural descriptions, a world as graph, not a collection of things that evolve in time.”

“in strongly interacting high-energy physics, it is doubtful that objects as individuated (using the Principle of Indiscernibles) by the invariant properties and relations definable in quantum field theory will be quanta at all.”

“don’t supposedly intrinsic properties of Bohmian particles like charge or mass (both gravitational and inertial mass) act, in experimental contexts, as if associated with the pilot wave rather than the particles?”[35]

**Argument V.**

**AV.1.**

**AV.2.**

**AV.3.**

**AV.C.**

“Chris Timpson and I Wallace (…) regard this as a major failure of Lewis’s doctrine of Humean supervenience, the doctrine that all facts about the world supervene on monadic properties of spacetime points and the spacetime relations between them: in our view, the entanglement between (say) spacetime regions A and B should be understood precisely as encoding certain irreducible relations between A and B.”[17], (p. 17)

#### 3.4. Decoherence-Based MWI

_{1}, will then be hopelessly out of phase relative to another position x

_{2}: then, from the relative ‘point of view’ of x

_{1}(plus the environmental states it is entangled with), other position states (plus their respective entangled environment) effectively disappear due to non-interference (for the record, while interference becomes negligibly small, it does not disappear totally. This is also why branching is regarded as a continuous process, and as a consequence, branch counting is best understood in a coarse-grained sense).

“Notice that it is not merely the linearity of quantum mechanics which allows us to interpret superpositions as instantiating multiple structures. Rather, it is the disappearance of interference terms between the relevant terms in those superpositions.”[39], (p. 68)

_{x1}+ βψ

_{x2}) ⊗ φ

_{0}→ αψ

_{x1}⊗ φ

_{x1}+ βψ

_{x2}⊗ φ

_{x2}.

_{0}(strictly speaking, such position eigenstates are non-normalizable delta-functions, hence unphysical. However, when putting limited resolutions of detectors into account, one ought to regard them as a mixture of position eigenstates, i.e., a ‘gaussian spikes’). As decoherences process in time, each conjunct on the right-hand side of the equation then expresses individually entangled states consisting of effectively two environmental states, φ

_{x1}and φ

_{x2}; one is entangled with measurement outcome αψ

_{x1}, while not interfering with βψ

_{x2}, and vice versa. For both particle position states ψ

_{x1}and ψ

_{x2}then exist as an entangled set, whereas each can be taken as a world; however, both are relatively out of phase to the other, thus they no longer interfere.

_{q}+ β |−˃

_{q}) ⊗ |0 ˃

_{a}⊗ |0 ˃

_{e}

_{q}|+ ˃

_{a}+ β|− ˃

_{q}|− ˃

_{a}) ⊗ |0 ˃

_{e}

_{q}|+ ˃

_{a}|+ ˃

_{e}+ β|− ˃

_{q}|− ˃

_{a}|− ˃

_{e}.

“So, in the case of chaos, ‘worlds’—that is, emergent quasi-classical systems—are constantly splitting from one another. And since the system’s state is always a mixture of reasonably localized wave-packets, the failure of classicality which we predicted for isolated chaotic systems will not occur here.”([39], p. 84)

## 4. Discussion

^{2}| and |β

^{2}| measure unequal ‘degrees of existence’, if α ≠ β. While being an interesting concept, I fear however that ‘degrees of existence’ is conceptually vague and potentially problematic. Here, an adaption of Lewisian ‘indexicality of actuality’ [50] might be a promising alternative. Then, ‘degrees of existence’ might not be absolute but an indexical or relational value depending on the location within the multiverse (however, discussing this goes beyond the scope of this review. At any rate, even if ‘degrees of existence’ is true, a MWI still follows, as the better part of the state vector, at least in terms of reasonable approximations, is ontologically on a par. Hence, then also, a constrained version of branches, one with somewhat vague ‘boundaries’, seemingly follows.)

^{2}|<|β

^{2}| holds for equation (17) within a particular branch, then relatively fewer sub-branches will exhibit |+ ˃

_{q}than |− ˃

_{q}. In other words, relative frequencies in terms of ratios can be given: “There may be no true number of the relevant microstates, in each case, but there may yet be true ratios.” [53] (as Saunders argues, instead of Vaidmanian ‘degrees of existence’, this may rather be an instance of [relative!] numbers of existence.). While Wallace argues in [39] that decoherence provides no well-defined notion of branch count, I would argue that it provides a reasonably well-defined branch count, in the same way it provides reasonably well-localized wave packets.

## 5. Conclusions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Huber, M.
Defending Many Worlds via Case Discrimination: An Attempt to Showcase the Conceptual Incoherence of Anti-Realist Interpretations and Relational Quantum Mechanics. *Quantum Rep.* **2023**, *5*, 345-369.
https://doi.org/10.3390/quantum5020023

**AMA Style**

Huber M.
Defending Many Worlds via Case Discrimination: An Attempt to Showcase the Conceptual Incoherence of Anti-Realist Interpretations and Relational Quantum Mechanics. *Quantum Reports*. 2023; 5(2):345-369.
https://doi.org/10.3390/quantum5020023

**Chicago/Turabian Style**

Huber, Michael.
2023. "Defending Many Worlds via Case Discrimination: An Attempt to Showcase the Conceptual Incoherence of Anti-Realist Interpretations and Relational Quantum Mechanics" *Quantum Reports* 5, no. 2: 345-369.
https://doi.org/10.3390/quantum5020023